Departure from Gaussian: The Waiting Time Statistics of X-Ray Solar Flares

Previous studies of the statistical behavior of solar flare waiting times are based on the assumptions of Gaussian and Poisson statistics, subject to central limit theorem restrictions. In this study, the results of a rescaled range analysis on the waiting times for two hard x-ray solar flare data sets are presented. The Hurst scaling parameter, H, for both data sets are well above 0.5, clearly indicating that the statistics of the data has departed from ordinary Brownian motion and is characterized by memory correlations. In addition, the distribution exponents, μ, when compared to the same values obtained from the relationship between the scaling parameter and μ for an asymmetric jump model, reveals that the waiting time distributions are characterized by Lévy statistics.